Statistics homework

Assignment 6

1. 60% of the student body at PSU is from the state of Pennsylvania (O), 30% are from

other states (O), and the remainder are international student (I). 20% of students from

Pennsylvania live in the dormitories, whereas, 50% of students from other states live in

the dormitories. Finally, 80% of the international students live in the dormitories.

a. What % of PSU students live in the dormitories?

b. Given that a student lives in the dormitory, what is the probability that she/he is an

international student?

c. Given that a student lives in the dormitory, what is the probability that she/he is from

Pennsylvania?

2. Calculate the following probabilities.

a. A six-sided die is tossed 3 times. What is the probability of observing three ones in a

row?

b. Suppose that 𝑃(𝐴 ∩ 𝐵) =0.30, and P(B)=0.60, then what is the probability of P(A) that makes events A and B independent events?

c. If P(A)=0.68, 𝑃(𝐴 ∪ 𝐵) =0.91, and 𝑃(𝐴 ∩ 𝐵)=0.35, then what is P(B)? d. If A and B are independent events with P(A)=0.38 and P(B)=0.55, then what is

P(A|B)?

3. James is a general contractor and has submitted two bids for two projects (A and B). The

probability of getting project A is 0.65, and the probability of getting project B is 0.77.

The probability of getting at least one of the projects is 0.90.

a. What is the probability that she will get both projects?

b. Are the events of getting the two projects mutually exclusive? Explain using

probabilities.

c. Are the two events independent? Explain using probabilities.